Chapter 1

Find the slope of the line through \(P\) and \(Q .\) \(P(0,0), Q(3,-1)\)

Solution? Determine whether the given value is a solution of the equation. \(1-[2-(3-x)]=4 x-(6+x)\) (a) \(x=2\) (b) \(x=4\)

Solve the equation both algebraically and graphically. $$x^{3}+16=0$$

Using Variables Express the given quantity in terms of the indicated variable. The sum of the squares of two consecutive integers; \(n=\) first integer of the two.

Complete the following table by stating whether the polynomial is a monomial, binomial, or trinomial; then list its terms and state its degree. $$\begin{array}{llll}\text { Polynomial } & \text { Type } & \text { Terms } & \text { Degree } \\ \hline -2 x^{2}+5 x-3 & & &\end{array}$$

Find the real and imaginary parts of the complex number. $$\frac{4+7 i}{2}$$

Find the domain of the expression. $$\frac{2 t^{2}-5}{3 t+6}$$

Real Numbers List the elements of the given set that are (a) natural numbers (b) integers (c) rational numbers (d) irrational numbers $$\left\\{1.3,1.3333 \ldots, \sqrt{5}, 5.34,-500,1 \frac{2}{3}, \sqrt{16}, \frac{246}{579},-\frac{20}{5}\right\\}$$

Write an equation that expresses the statement. \(y\) is proportional to \(s\) and inversely proportional to \(t\).

Write each radical expression using exponents, and each exponential expression using radicals. Radical expression = ? Exponential expression = \(4^{2 / 3}\)

Find the slope of the line through \(P\) and \(Q .\) \(P(2,-2), Q(7,-1)\)

Let \(S=\left\\{-5,-1,0, \frac{2}{3}, \frac{5}{6}, 1, \sqrt{5}, 3,5\right\\}\) Determine which elements of \(S\) satisfy the inequality. $$\frac{1}{x} \leq \frac{1}{2}$$

Solution? Determine whether the given value is a solution of the equation. \(\frac{1}{x}-\frac{1}{x-4}=1\) (a) \(x=2\) (b) \(x=4\)

Using Variables Express the given quantity in terms of the indicated variable. The average of three test scores if the first two scores are 78 and \(82 ; \quad s=\) third test score.

Solve the equation both algebraically and graphically. $$x^{2}+9=0$$

Complete the following table by stating whether the polynomial is a monomial, binomial, or trinomial; then list its terms and state its degree. $$\begin{array}{llll}\text { Polynomial } & \text { Type } & \text { Terms } & \text { Degree } \\ \hline -8 & & &\end{array}$$

Find the real and imaginary parts of the complex number. $$3$$

Find the domain of the expression. $$\sqrt{x+3}$$

Properties of Real Numbers State the property of real numbers being used. $$3+7=7+3$$

Write an equation that expresses the statement. \(P\) varies inversely as \(T\).

Write each radical expression using exponents, and each exponential expression using radicals. Radical expression = ? Exponential expression = \(10^{-3 / 2}\)

Find the slope of the line through \(P\) and \(Q .\) \(P(-5,1), Q(3,-2)\)

Let \(S=\left\\{-5,-1,0, \frac{2}{3}, \frac{5}{6}, 1, \sqrt{5}, 3,5\right\\}\) Determine which elements of \(S\) satisfy the inequality. $$x^{2}+2 < 4$$

Solution? Determine whether the given value is a solution of the equation. \(\frac{x^{3 / 2}}{x-6}=x-8\) (a) \(x=4\) (b) \(x=8\)

Solve the equation both algebraically and graphically. $$x^{2}+3=2 x$$

Using Variables Express the given quantity in terms of the indicated variable. The average of four quiz scores if each of the first three scores is \(8 ; \quad q=\) fourth quiz score.

Complete the following table by stating whether the polynomial is a monomial, binomial, or trinomial; then list its terms and state its degree. $$\begin{array}{llll}\text { Polynomial } & \text { Type } & \text { Terms } & \text { Degree } \\ \hline \frac{1}{2} x^{7} & & &\end{array}$$

Find the real and imaginary parts of the complex number. $$-\frac{1}{2}$$

Find the domain of the expression. $$\frac{1}{\sqrt{x-1}}$$

Properties of Real Numbers State the property of real numbers being used. $$4(2+3)=(2+3) 4$$

Find the slope of the line through \(P\) and \(Q .\) \(P(5,4), Q(0,4)\)

Write an equation that expresses the statement. \(z\) is proportional to the square root of \(y\).

Write each radical expression using exponents, and each exponential expression using radicals. Radical expression = \(\sqrt[5]{5^{3}}\) Exponential expression = ?

Plot the given points in a coordinate plane. $$(0,5),(-1,0),(-1,-2),\left(\frac{1}{2}, \frac{2}{3}\right)$$

Linear Equations The given equation is either linear or equivalent to a linear equation. Solve the equation. $$5 x-6=14$$

Linear Inequalities Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$2 x \leq 7$$

Using Variables Express the given quantity in terms of the indicated variable. The interest obtained after 1 year on an investment at \(2 \frac{1}{2} \%\) simple interest per year; \(\quad x=\) number of dollars invested.

Solve the equation both algebraically and graphically. $$16 x^{4}=625$$

Complete the following table by stating whether the polynomial is a monomial, binomial, or trinomial; then list its terms and state its degree. $$\begin{array}{llll}\text { Polynomial } & \text { Type } & \text { Terms } & \text { Degree } \\ \hline x-x^{2}+x^{3}-x^{4} & & &\end{array}$$

Find the real and imaginary parts of the complex number. $$-\frac{2}{3} i$$

Find the domain of the expression. $$\frac{x^{2}+1}{x^{2}-x-2}$$

Properties of Real Numbers State the property of real numbers being used. $$(x+2 y)+3 z=x+(2 y+3 z)$$

Find the slope of the line through \(P\) and \(Q .\) \(P(4,3), Q(1,-1)\)

Write an equation that expresses the statement. \(A\) is proportional to the square of \(x\) and inversely proportional to the cube of \(t\).

Plot the given points in a coordinate plane. $$(-5,0),(2,0),(2.6,-1.3),(-2.5,3.5)$$

Linear Inequalities Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$-4 x \geq 10$$

Linear Equations The given equation is either linear or equivalent to a linear equation. Solve the equation. $$3 x+4=7$$

Using Variables Express the given quantity in terms of the indicated variable. The total rent paid for an apartment if the rent is \(\$ 795\) a month; \(n=\) number of months.

Solve the equation both algebraically and graphically. $$2 x^{5}-243=0$$

Complete the following table by stating whether the polynomial is a monomial, binomial, or trinomial; then list its terms and state its degree. $$\begin{array}{llll}\text { Polynomial } & \text { Type } & \text { Terms } & \text { Degree } \\ \hline \sqrt{2} x-\sqrt{3} & & &\end{array}$$